Diffusion models have shown exceptional capabilities in generating realistic videos. Yet, their training has been predominantly confined to offline environments where models can repeatedly train on i.i.d. data to convergence. This work explores the feasibility of training diffusion models from a semantically continuous video stream, where correlated video frames sequentially arrive one at a time. To investigate this, we introduce two novel continual video generative modeling benchmarks, Lifelong Bouncing Balls and Windows 95 Maze Screensaver, each containing over a million video frames generated from navigating stationary environments. Surprisingly, our experiments show that diffusion models can be effectively trained online using experience replay, achieving performance comparable to models trained with i.i.d. samples given the same number of gradient steps.